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0.0

Jun 28, 2018
06/18

by
Sudev Naduvath

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For a positive integer $n$, let $\mZ$ be the set of all non-negative integers modulo $n$ and $\sP(\mZ)$ be its power set. A modular sumset valuation or a modular sumset labeling of a given graph $G$ is an injective function $f:V(G) \to \sP(\mZ)$ such that the induced function $f^+:E(G) \to \sP(\mZ)$ defined by $f^+ (uv) = f(u)+ f(v)$. A sumset indexer of a graph $G$ is an injective sumset valued function $f:V(G) \to \sP(\mZ)$ such that the induced function $f^+:E(G) \to \sP(\mZ)$ is also...

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1508.00319

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0.0

Jun 28, 2018
06/18

by
Johan Kok; Naduvath Sudev

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The studies on $b$-chromatic number attracted much interest since its introduction. In this paper, we discuss the $b$-chromatic number of certain classes of graphs and digraphs. The notion of a new general family of graphs called the Chithra graphs of a graph $G$ are also introduced.

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1511.00680

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Jun 28, 2018
06/18

by
Faruk Karaaslan

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In this paper, we propose three similarity measure methods for single valued neutrosophic refined sets and interval neutrosophic refined sets based on Jaccard, Dice and Cosine similarity measures of single valued neutrosophic sets and interval neutrosophic sets. Furthermore, we suggest two multi-criteria decision making method under single valued neutrosophic refined environment and interval neutrosophic refined environment, and give applications of proposed multi-criteria decision making...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1512.03687

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0.0

Jun 29, 2018
06/18

by
Naduvath Sudev

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Let $X$ be a non-empty set and $\sP(X)$ be its power set. A set-valuation or a set-labeling of a given graph $G$ is an injective function $f:V(G) \to \sP(X)$ such that the induced function $f^{\ast}:E(G) \to \sP(X)$ defined by $f^{\ast} (uv) = f(u)\ast f(v)$, where $\ast$ is a binary operation on sets. A set-indexer of a graph $G$ is an injective set-valued function $f:V(G) \to \sP(X)$ such that the induced function $f^{\ast}:E(G) \to \sP(X)$ is also injective. In this paper, two types of...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1601.02662

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3.0

Jun 28, 2018
06/18

by
Marcoen J. T. F. Cabbolet

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Recently Feferman (Rev. Symb. Logic 6: 6-15, 2013) has outlined a program for the development of a foundation for naive category theory. While Ernst (ibid. 8: 306-327, 2015) has shown that the resulting axiomatic system is still inconsistent, the purpose of this note is to show that nevertheless some foundation has to be developed before naive category theory can replace axiomatic set theory as a foundational theory for mathematics. It is argued that in naive category theory currently a...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1509.08814

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0.0

Jun 28, 2018
06/18

by
Nikos Bagis

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In this article we give solution of the general quintic equation by means of the Rogers-Ramanujan continued fraction. More precisely we express a root of the quintic as a known algebraic function of the Rogers-Ramanujan continued fraction.

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1510.00068

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0.0

Jun 28, 2018
06/18

by
N. K. Sudev; C. Susanth; K. P. Chithra; Johan Kok; Sunny Joseph Kalayathankal

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Let $S=S_1S_2S_3\ldots S_n$ be a finite string. Write $S$ in the form $XYY\ldots Y=XY^k$, consisting of a prefix $X$ (which may be empty), followed by $k$ copies of a non-empty string $Y$. Then, the greatest value of this integer $k$ is called the curling number of $S$ and is denoted by $cn(S)$. Let the degree sequence of the graph $G$ be written as a string of identity curling subsequences say, $X^{k_1}_1\circ X^{k_2}_2\circ X^{k_3}_3 \ldots \circ X^{k_l}_l$. The compound curling number of...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1510.01271

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0.0

Jun 28, 2018
06/18

by
Angsuman Das

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In this paper, we introduce a graph structure, called non-zero component graph on finite dimensional vector spaces. We show that the graph is connected and find its domination number and independence number. We also study the inter-relationship between vector space isomorphisms and graph isomorphisms and it is shown that two graphs are isomorphic if and only if the corresponding vector spaces are so. Finally, we determine the degree of each vertex in case the base field is finite.

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1506.04905

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7.0

Jun 28, 2018
06/18

by
Nianrong Feng; Yongzheng Wang; Ruixin Wu

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From Riemann's paper and nachlass, we obtained three conclusions about the zero of the Riemann zeta-function. First, we sort out the complete process of Riemann's proof of his hypothesis. In addition, a formula is revealed from a long-overlooked function, $$\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)=2\Re(\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})f(s))\qquad\Re(s)=1/2,$$ to compute the number of zeros of $\zeta(1/2+it)$. Furthermore, the evidence shows that Riemann had proved that all of zeros of...

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1508.02932

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0.0

Jun 26, 2018
06/18

by
Maurice Margenstern; Yaroslav D. Sergeyev

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The twin primes conjecture is a very old problem. Tacitly it is supposed that the primes it deals with are finite. In the present paper we consider three problems that are not related to finite primes but deal with infinite integers. The main tool of our investigation is a numeral system proposed recently that allows one to express various infinities and infinitesimals easily and by a finite number of symbols. The problems under consideration are the following and for all of them we give...

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1501.03051

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1.0

Jun 27, 2018
06/18

by
Mike Winkler

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Let $\sigma_n=\lfloor1+n\cdot\log_23\rfloor$. For the Collatz 3x + 1 function exists for each $n\in\mathbb{N}$ a set of different residue classes $(mod\ 2^{\sigma_n})$ of starting numbers $s$ with finite stopping time $\sigma(s)=\sigma_n$. Let $z_n$ be the number of these residue classes for each $n\geq0$ as listed in the OEIS as A100982. It is conjectured that for each $n\geq4$ the value of $z_n$ is given by the formula \begin{align*}...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1504.00212

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1.0

Jun 28, 2018
06/18

by
Susanth C.; Sunny Joseph Kalayathankal; N. K. Sudev; K. P. Chithra; Johan Kok

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Given a finite nonempty sequence $S$ of integers, write it as $XY^k$, where $Y^k$ is a power of greatest exponent that is a suffix of $S$: this $k$ is the curling number of $S$. The concept of curling number of sequences has already been extended to the degree sequences of graphs to define the curling number of a graph. In this paper we study the curling number of graph powers, graph products and certain other graph operations.

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1509.00220

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1.0

Jun 28, 2018
06/18

by
Alok Kumar

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In this paper, we obtained some global approximation results for general Gamma type operators.

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1508.06883

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4.0

Jun 28, 2018
06/18

by
Shlomo Jacobi

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This manuscript introduces $J_3$-numbers, a seemingly missing three-dimensional intermediate between complex numbers related to points in the Cartesian coordinate plane and Hamilton's quaternions in the 4D space. The current development is based on a rotoreflection operator $j$ in $\mathbb{R}^3$ that induces a novel $\circledast$-multiplication of triples which turns out to be associative, distributive and commutative. This allows one to regard a point in $\mathbb{R}^3$ as the three-component...

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1509.01459

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6.0

Jun 27, 2018
06/18

by
N. K. Sudev; K. A. Germina; K. P. Chithra

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For a non-empty ground set $X$, finite or infinite, the {\em set-valuation} or {\em set-labeling} of a given graph $G$ is an injective function $f:V(G) \to \mathcal{P}(X)$, where $\mathcal{P}(X)$ is the power set of the set $X$. A set-indexer of a graph $G$ is an injective set-valued function $f:V(G) \to \mathcal{P}(X)$ such that the function $f^{\ast}:E(G)\to \mathcal{P}(X)-\{\emptyset\}$ defined by $f^{\ast}(uv) = f(u){\ast} f(v)$ for every $uv{\in} E(G)$ is also injective., where $\ast$ is a...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1504.07132

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7.0

Jun 26, 2018
06/18

by
Masum Billal

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We dedicate this paper to investigate the most generalized form of Fibonacci Sequence, one of the most studied sections of the mathematical literature. One can notice that, we have discussed even a more general form of the conventional one. Although it seems the topic in the first section has already been covered before, but we present a different proof here. Later I found out that, the auxiliary theorem used in the first section was proven and even generalized further by F. T. Howard. Thanks...

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1502.06869

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2.0

Jun 27, 2018
06/18

by
Nicolas Le Bihan

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Second order circularity, also called properness, for complex random variables is a well known and studied concept. In the case of quaternion random variables, some extensions have been proposed, leading to applications in quaternion signal processing (detection, filtering, estimation). Just like in the complex case, circularity for a quaternion-valued random variable is related to the symmetries of its probability density function. As a consequence, properness of quaternion random variables...

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1505.06182

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Jun 27, 2018
06/18

by
Giuliano G. La Guardia; Ana Lucia Pereira Baccon

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A magic square of order n is an nxn square (matrix) whose entries are distinct nonnegative integers such that the sum of the numbers of any row and column is the same number, the magic constant. In this paper we introduce the concept of pseudo magic squares, i.e., magic squares defined over the ring of integers, without the restriction of distinct numbers. Additionally, we generalize this new concept by introducing a group (ring) structure over it. This new approach can provide useful tools in...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1504.05642

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2.0

Jun 27, 2018
06/18

by
Agostino Prástaro

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By introducing a new point of view in Algebraic Topology relating elliptic curves in $\mathbb{R}^2$ and suitable bordism groups, the congruent number problem is solved showing that the Tunnell's theorem is also sufficient. This could be considered also an indirect proof that the Birch Swinnerton-Dyer conjecture is true.

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1504.07507

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5.0

Jun 28, 2018
06/18

by
Jailton C. Ferreira

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A proof that there is no $3 \times 3$ magic square constructed with nine distinct square numbers is given.

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1506.06621

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1.0

Jun 28, 2018
06/18

by
N. K. Sudev; K. P. Chithra; K. A. Germina

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Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ is defined by $f^+ (uv) = f(u)+ f(v)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. In this paper, we introduce the notion of a particular type of integer additive set-indexers called...

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1507.02173

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6.0

Jun 28, 2018
06/18

by
Sergey Loyka

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A counter-example to lower bounds for the singular values of the sum of two matrices in [1] and [2] is given. Correct forms of the bounds are pointed out.

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1507.06630

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2.0

Jun 28, 2018
06/18

by
Ricardo Almeida; Nuno R. O. Bastos; M. Teresa T. Monteiro

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This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1511.06202

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1.0

Jun 29, 2018
06/18

by
Dong-hua Luo; Cheng-qun Pang

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In this paper, we point out that many Jacobi elliptic function solutions to non-linear differential equation(NDE) can be transformed each other via the modulus and phase transformation of Jacobi elliptic function. Therefore these solutions are equivalent. We investigate equivalent of the Jacobi elliptic function solutions of Korteweg-de Vries (mKdV) equation as a example.

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1601.03245

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2.0

Jun 26, 2018
06/18

by
Thomas Havenith; Sebastian Scholtes

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When computing the average speed of a car over different time periods from given GPS data, it is conventional wisdom that the maximal average speed over all time intervals of fixed length decreases if the interval length increases. However, this intuition is wrong. We investigate this phenomenon and make rigorous in which sense this intuition is still true.

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1501.06391

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1.0

Jun 28, 2018
06/18

by
Hirokazu Nishimura; Hirowaki Takamiya

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We have studied the infinitesimal Baker-Campbell-Hausdorff formula up to n=4 (Math. Appl. 2 (2013), 61-91). In this note we correct some errors in our calculation for n=4 and presents the calculation for n=5 by using Mathematica.

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1507.01453

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0.0

Jun 28, 2018
06/18

by
Niovi Kehayopulu

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This is about the paper by Thawhat Changphas and Nawamin Phaipong in Quasigroups and Related Systems 22 (2014), 193--200.

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1510.02326

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0.0

Jun 28, 2018
06/18

by
Samir Brahim Belhaouari

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The idea of generating prime numbers through sequence of sets of co-primes was the starting point of this paper that ends up by proving two conjectures, the existence of infinitely many twin primes and the Goldbach conjecture. The main idea of our approach is summarized on the creation and on the analyzing sequence of sets of distinct co-primes with the first $n$ primes, $\left\{ p_i :\, i\leq n \right\}$, and the important properties of the modulus linear combination of the co-prime sets,...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1512.00970

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1.0

Jun 26, 2018
06/18

by
Niovi Kehayopulu

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We characterize the fuzzy left (resp. right) ideals, the fuzzy ideals and the fuzzy prime (resp. semiprime) ideals of an ordered $\Gamma$-groupoid $M$ in terms of level subsets and we prove that the cartesian product of two fuzzy left (resp. right) ideals of $M$ is a fuzzy left (resp. right) ideal of $M\times M$, and the cartesian product of two fuzzy prime (resp. semiprime) ideals of $M$ is a fuzzy prime (resp. semiprime) ideal of $M\times M$. As a result, if $\mu$ and $\sigma$ are fuzzy left...

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1501.03955

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0.0

Jun 28, 2018
06/18

by
Jonathan W. Roginski; Ralucca M. Gera; Erik C. Rye

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The newly introduced neighborhood matrix extends the power of adjacency and distance matrices to describe the topology of graphs. The adjacency matrix enumerates which pairs of vertices share an edge and it may be summarized by the degree sequence, a list of the adjacency matrix row sums. The distance matrix shows more information, namely the length of shortest paths between vertex pairs. We introduce and explore the neighborhood matrix, which we have found to be an analog to the distance...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1510.06952

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2.0

Jun 28, 2018
06/18

by
Huan Huang

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In this paper, it shows that for each fuzzy set $u$ on $\mathbb{R}^m$, the set $D(u)$ is at most countable. Based on this, it modifies the proof of assertion (I) in step 2 of the sufficiency part of Theorem 4.1 in paper: Characterizations of compact sets in fuzzy sets spaces with $L_p$ metric, http://arxiv.org/abs/1509.00447.

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1510.06953

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0.0

Jun 28, 2018
06/18

by
A. Tayebi; T. Tabatabaeifar

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In this paper, we study the reversibility of Riemann curvature and Ricci curvature for the Matsumoto metric and prove three global results. First, we prove that a Matsumoto metric is R-reversible if and only if it is R-quadratic. Then we show that a Matsumoto metric is Ricci-reversible if and only if it is Ricci-quadratic. Finally, we prove that every weakly Einstein Matsumoto metric is Ricci-reversible.

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1511.00927

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0.0

Jun 28, 2018
06/18

by
Niovi Kehayopulu; Michael Tsingelis

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We characterize the intra-regular $\Gamma$-semigroups and the left regular $\Gamma$-semigroups $M$ in which $x\Gamma M\subseteq M\Gamma x$ for every $x\in M$ in terms of filters and we prove, among others, that every intra-regular $\Gamma$-semigroup is decomposable into simple components, and every $\Gamma$-semigroup $M$ for which $x\Gamma M\subseteq M\Gamma x$ is left regular, is decomposable into left simple components.

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1511.07783

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0.0

Jun 28, 2018
06/18

by
Ricardo Almeida; Nuno R. O. Bastos

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The objective of this paper is to present an approximation formula for the Katugampola fractional integral, that allows us to solve fractional problems with dependence on this type of fractional operator. The formula only depends on first-order derivatives, and thus we convert the fractional problem into a standard one. With some examples we show the accuracy of the method, and then we present the utility of the method by solving a fractional integral equation.

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1512.03791

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0.0

Jun 28, 2018
06/18

by
Gyula Lakos

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The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case $n=2$, and FQ conform-operations in the case $n=3$. In this second part we show some arithmetically constructible examples of FQ operations ($n=2$), concentrating on monoaxiality, related extensions, and (hyper)scaling.

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1512.03716

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0.0

Jun 29, 2018
06/18

by
Daochun Sun; Yingying Huo; Yinying Kong; Fujie Chai

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In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the definition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1602.03382

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3.0

Jun 27, 2018
06/18

by
N. A. Carella

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An asymptotic formula for the number of integers with the primitive root 2, and a generalized Artin primitive root conjecture for composite integers is presented here.

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1504.00843

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4.0

Jun 27, 2018
06/18

by
Aleks Kleyn

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Let $A$ be Banach algebra over commutative ring $D$. The map $f:A\rightarrow A\ $ is called differentiable in the Gateaux sense, if $$f(x+a)-f(x)=\partial f(x)\circ a+o(a)$$ where the Gateaux derivative $\partial f(x)$ of map $f$ is linear map of increment $a$ and $o$ is such continuous map that $$ \lim_{a\rightarrow 0}\frac{|o(a)|}{|a|}=0 $$ Assuming that we defined the Gateaux derivative $\partial^{n-1} f(x)$ of order $n-1$, we define $$ \partial^n f(x)\circ(a_1\otimes...\otimes a_n)...

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1505.03625

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3.0

Jun 26, 2018
06/18

by
Konstantinos N. Gaitanas

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We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1501.03113

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Jun 26, 2018
06/18

by
Charles G. Gunn

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The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief review of PGA, the article focuses on $\mathbf{P}(\mathbb{R}^*_{2,0,1})$, the PGA for euclidean plane geometry. It first explores the geometric product involving pairs and triples of basic elements (points and lines), establishing a wealth of fundamental metric...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1501.06511

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2.0

Jun 28, 2018
06/18

by
H. S. Shukla; V. K. Chaubey; Arunima Mishra

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In the present paper we have considered h-Randers conformal change of a Finsler metric $ L $, which is defined as \begin{center}$ L(x,y)\rightarrow \bar{L}(x, y)=e^{\sigma(x)}L(x, y)+\beta (x, y), \end{center} where $ \sigma(x) $ is a function of x, $\beta(x, y) = b_{i}(x, y)y^{i}$ is a 1- form on $M^{n}$ and $b_{i}$ satisfies the condition of being an h-vector. We have obtained the expressions for geodesic spray coefficients under this change. Further we have studied some special Finsler...

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1506.05102

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2.0

Jun 26, 2018
06/18

by
Adrian Sescu

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In this work, nonreflecting boundary conditions in generalized three-dimensional curvilinear coordinates are derived, relying on the original analysis that was done in Cartesian two-dimensional coordinates by Giles (AIAA Journal, 28.12, 2050-2058, 1990). A thorough Fourier analysis of the linearized Euler equation is performed to determine the eigenvalues and the eigenvectors that are then used to derive the appropriate inflow and outflow boundary conditions. The analysis lacks rigorous proof...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1501.06392

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7.0

Jun 27, 2018
06/18

by
Chelton D. Evans; William K. Pattinson

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Integration at a point is a new kind of integration derived from integration over an interval in infinitesimal and infinity domains which are spaces larger than the reals. Consider a continuous monotonic divergent function that is continually increasing. Apply the fundamental theorem of calculus. The integral is a difference of the function integrated at the end points. If one of these point integrals is much-greater-than the other in magnitude delete it by non-reversible arithmetic. We call...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1503.00817

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6.0

Jun 27, 2018
06/18

by
N. A. Carella

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This note generalizes the Fibonacci primitive roots to the set of integers. An asymptotic formula for counting the number of integers with such primitive root is introduced here.

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1505.05519

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2.0

Jun 27, 2018
06/18

by
Johan Kok; K. P. Chithra; N. K. Sudev; C. Susanth

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A \textit{primitive hole} of a graph $G$ is a cycle of length $3$ in $G$. The number of primitive holes in a given graph $G$ is called the primitive hole number of that graph $G$. The primitive degree of a vertex $v$ of a given graph $G$ is the number of primitive holes incident on the vertex $v$. In this paper, we introduce the notion of set-graphs and study the properties and characteristics of set-graphs. We also check the primitive hole number and primitive degree of set-graphs. Interesting...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1504.02703

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Jun 27, 2018
06/18

by
Mustafa Ozdemir

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Elliptical rotation is the motion of a point on an ellipse through some angle about a vector. The purpose of this paper is to examine the generation of elliptical rotations and to interpret the motion of a point on an elipsoid using elliptic inner product and elliptic vector product. To generate an elliptical rotation matrix, first we define an elliptical ortogonal matrix and an elliptical skew symmetric matrix using the associated inner product. Then we use elliptic versions of the famous...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1503.07895

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2.0

Jun 26, 2018
06/18

by
Aleks Kleyn

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Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book. To consider this definition from more general point of view I started the book from consideration of Cartesian product of representations. Polymorphism of representations is a map of Cartesian product of representations which is a morphism of representations with respect to each separate independent...

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1502.04063

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Jun 27, 2018
06/18

by
Tulay Erisir; Mehmet Ali Gungor; Soley Ersoy

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In this paper, one-parameter planar motion in the generalised complex plane (or p-complex plane) ${C_p} = \left\{ {x + iy: x,y \in R, {i^2} = p} \right\}$ which is defined as a system of generalised complex numbers is studied. Firstly, generalised Bobillier formula is obtained by using the geometric interpretation of generalised Euler-Savary formula in the p-complex plane. Moreover, it is shown that the Bobillier formula may be obtained by an alternative method without the use of Euler-Savary...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1503.01616

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Jun 27, 2018
06/18

by
Michael A. Idowu

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Set out here are some fundamental theories that may be regarded as newly discovered metamathematics of the odd integers in relation to the Collatz conjecture (also called the 3x+1 problem). Originally motivated by the requirement to invent a new optimised integer factorisation method, this foundational paper primarily focuses on the foundation, formalisation and presentation of a new theoretical framework (schema or blueprint) of a Collatz based number system. The proposed framework is based on...

Topics: General Mathematics, Mathematics

Source: http://arxiv.org/abs/1503.04661

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Jun 27, 2018
06/18

by
Hakan Simsek; Mustafa Özdemir

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In this paper, we study the differential geometry of null Cartan curves under the similarity transformations in the Minkowski space-time. Besides, we extend the fundamental theorem for a null Cartan curve according to a similarity motion. We find the equations of all self-similar null curves which is given its shape Cartan curvatures.

Topics: Mathematics, General Mathematics

Source: http://arxiv.org/abs/1505.04716